Question

Cos²A+ Sin^2A. Cos2B = Cos²B + sin²B. Cos2A prove​

Answer 1

Answer:

L.H.S=cos^2A+sin^2A.cos2B

=cos^2A+sin^2A.(1-2sin^2B) [ since, 

cos2A=1-2sin^2A]

=cos^2A+sin^2A-2.sin^2A.sin^2B

=1-2.sin^2A.sin^2B [ since, sin^2A+cos^2A=1]

R. H. S=cos^2B+sin^2B.cos2A

=cos^2B+sin^2B.(1-2sin^2A)

=cos^2B+sin^2B-2.sin^2A.sin^2B

=1-2.sin^2A.sin^2B

L. H. S = R.H.S

 hence proved

Answer 2

Your answer :-

LHS=(sinAcosB) 2−(cosAsinB) 2

=(sinAcosB+cosAsinB)(sinAcosB−cosAsinB)

=sin(A+B)sin(A−B)

=sin

2 A−sin

2 B =RHS

Hence proved

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